By scalar-valued financial instrument (“SFI”) I mean a financial instrument whose value is completely represented as a magnitude of a currency. Note that the value of an SFI may be unknown, subject to measurement error, or valued differently at different times and places and by different people (“value assessors”). Nonetheless, despite disagreements, uncertainties, and variability in value, a scalar-valued financial instrument has, by definition, a unique value in a given context. The context of a valuation may include time, place, value assessor, actual owner, hypothetical owner, other interested parties, or other relevant factors such as interest rates, exchange rates, and other financial or economic variables.
SFIs may be real or imaginary:                A real SFI is an SFI whose value is completely represented in a real currency, e.g., U.S. dollars. Examples of real SFIs include, United States Savings Bonds, shares of common stock in a corporation, and IOUs. Currencies such as euros, dollars, and yen are themselves special kinds of real SFIs.        An imaginary SFI is an SFI whose value is represented in an imaginary currency. An imaginary currency is a currency with no actual value that may be used to play a game. An example is the currency used to play the game of Monopoly®. Financial instruments denominated in “Monopoly money” or some other “play money” would be examples of imaginary SFIs.        
All existing financial instruments are scalar-valued:                Commerce and games that are played for money use real currencies or other real SFIs.        Other games sometimes use imaginary SFIs, typically “play money.”        
Considered as commodities, games are purchased and sold using real currencies. In particular, “play money” may be bought or sold with real money. More generally, real SFIs may be traded for imaginary SFIs.
There are several contexts in which it would be useful to have a different type of financial instrument that extends the concept of financial instrument beyond the realm of scalar values. As explained in the next section, these contexts include:                Education        Rehabilitation        Recreation        Commerce        
Scalar values are enormously useful, enabling global commerce and providing a method of score-keeping in games that use either real money or play money. Nonetheless, value is not always adequately represented in scalar terms; values don't always line up on a single scale.
Human abilities to imagine, to simulate, or to create virtual worlds are examples of contexts in which non-scalar values may operate. All humans have the ability to imagine, engaging in “what if” exercises of varying degrees of sophistication and likelihood. The scalar model of value forces us to segregate our imagination from the world. This results in a misrepresentation of the relationship between the virtual and the real, with enormous consequences for our health and well-being, and for the health and well-being of those around us.
By reconnecting the domain of imaginary values with the domain of real values, and extending such domains to even more elaborate structures, we will be able to capture much more of the complexity of the world than we do at present. Such structures can help us learn better, overcome bad habits, and can act as a spur to creativity and economic growth.